Misha Verbitsky
Calibrations in hyperkahler geometry.
Ср, 09/08/2010 - 15:01 — SomNambulAuthors: Misha Verbitsky, Gueo Grantcharov
Subjects: Differential Geometry
AbstractWe describe a family of calibrations arising naturally on a hyperk\"ahler
manifold $M$. These calibrations calibrate the holomorphic Lagrangian,
holomorphic isotropic and holomorphic coisotropic subvarieties. When $M$ is an
HKT (hyperkaehler with torsion) manifold with holonomy $SL(n, {\Bbb H})$, we
construct another family of calibrations $\Phi_i$, which calibrates holomorphic
Lagrangian and holomorphic coisotropic subvarieties. The calibrations $\Phi_i$
are (generally speaking) not parallel with respect to any torsion-free
connection on $M$.A report on locally conformally K\"ahler manifolds.
Пт, 02/19/2010 - 16:01 — SomNambulAuthors: Misha Verbitsky, Liviu Ornea
Subjects: Differential Geometry
AbstractWe present an overview of recent results in locally conformally K\"ahler
geometry, with focus on the topological properties which obstruct the existence
of such structures on compact manifolds.A global Torelli theorem for hyperkahler manifolds.
Пнд, 08/31/2009 - 17:16 — SomNambulAuthors: Misha Verbitsky
Subjects: Algebraic Geometry
AbstractA mapping class group of an oriented manifold is a quotient of its
diffeomorphism group by the isotopies. We compute a mapping class group of a
hypekahler manifold $M$, showing that it is commensurable to an arithmetic
subgroup in SO(3, b_2-3). A Teichmuller space of $M$ is a space of complex
structures on $M$ up to isotopies.- Читать далее
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